Extending and Implementing the Stable Model Semantics

TL;DR

This paper develops an algorithm for computing stable model semantics of logic programs, extends it to more expressive rules, and introduces efficient implementation techniques including lookahead and heuristics, with empirical comparisons to satisfiability solvers.

Contribution

It presents an extended algorithm for stable model semantics that handles more expressive rules and incorporates efficient implementation techniques like lookahead and heuristics.

Findings

Heuristic improvements can be achieved by breaking ties.

Stable model semantics often produce more compact representations than propositional logic.

The system outperforms some satisfiability solvers in certain cases.

Abstract

An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of efficient implementation techniques. In particular, an implementation of lookahead that safely avoids testing every literal for failure and that makes the use of lookahead feasible is presented. In addition, a good heuristic is derived from the principle that the search space should be minimized. Due to the lack of competitive algorithms and implementations for the computation of stable models, the system is compared with three satisfiability solvers. This shows that the heuristic can be improved by breaking ties, but leaves open the question of how to break them. It also demonstrates that the more expressive rules of the stable model semantics make the semantics clearly preferable over propositional logic when a problem has a more compact logic program representation. Conjunctive normal form representations are never more compact than logic program ones.